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Organised in partnership with the  Clay Mathematics Institute



* Includes coffee breaks and lunch.

19th School on Interactions Between Dynamical Systems and Partial Differential Equations (JISD2023)

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Advanced course / School
From July 03, 2023
to July 07, 2023

Registration includes coffee breaks and lunch.

The School will take place at the AUDITORIUM of the CRM.

Registration deadline 04 / 06 / 2023


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The School on Interactions between Dynamical Systems and Partial Differential Equations (JISD) is an international summer school that takes place at the School of Mathematics and Statistics of the Universitat Politècnica de Catalunya (UPC) since 2002. The last four editions have been held at the Centre de Recerca Matemàtica (CRM).
The JISD is an annual meeting between experts and young researchers in Dynamical Systems and Partial Differential Equations (PDEs). It is designed to encourage and enhance exchange of knowledge and methods, with the goal of advancing the study of cutting edge problems in the aforesaid fields of mathematics and with the aim of fostering the interaction among the participants. The symposium is aimed at local researchers, as well as scientists from the rest of Spain and foreign countries. It is organized into four advanced courses of about 7 hours and complemented by a poster session by young researchers. Throughout the latest editions the attendance numbers have ranged between 60 and 100 participants, mostly internationals.
A primary objective of the JISD is to attract talented young researchers who can present a poster to put them in condition to benefit from the exposure to world-leading experts, and help them establish working relationships that could prove critical for their short and long term success. An especially strong effort has been devoted in past years to encourage the participation of undergraduates, PhDs and postdocs from developing countries and, more generally, young researchers who may encounter difficulties in accessing an adequate financial support. 


Transfer operators and anisotropic spaces for Sinai billiards by Prof. Viviane Baladi (CNRS, France)

We will present an approach to the statistical properties of two-dimensional dispersive billiards (discrete and continuous-time) using transfer operators acting on anisotropic Banach spaces of distributions. After recalling some classical background (Bunimovich, Sinai, Chernov, etc) based on other approaches, we will survey results by Demers, Zhang, Liverani, etc, joint work with Demers and Liverani on the SRB measure of flows, joint work with Demers on the measure of maximal entropy and other equilibrium states of maps, and joint work with Carrand and Demers on the measure of maximal entropy for flows.

The regularity theory for Bernoulli type free boundary problems by Prof. Guido de Philippis (Courant Institute, US)
I will present an overview on the regularity theory for Bernoulli like free boundary problem, starting from the seminal work of Allt-Caffarelli in the 80’s to the recent developments obtained in collaboration with L. Spolaor and B. Velichkov.
Dynamical spectral determination and rigidity by Prof. Jacopo de Simoi (University of Toronto, Canada)
The classical inverse problem asks to what extent it is possible to determine the shape of a domain D of the real plane (or of a surface), by the knowledge of all eigenvalues of the Laplace operator on D with assigned boundary conditions. A dynamical version of this question can be stated by replacing the set of eigenvalues of the Laplacian with the Length spectrum, that is the set of all lengths of all possible closed billiard orbits on D (or all closed geodesics in the case of manifolds). In these lectures, we will show the deep connection between the Laplace and the dynamical problem, we will present in detail some results on the dynamical side and explore the possible outcomes of the current research in this direction.
The obstacle problem: regularity of the free boundary and analysis of singularities by Prof. Joaquim Serra (ETH Zürich, Switzerland)
The classical obstacle problem is a very paradigmatic free boundary problem with several applications in physics, probability, potential theory, finance, etc. It is equivalent, after certain transformations, to other well-known free boundary problems such as the Stefan problem.
The goal of the course will be to give an introduction to the regularity theory for the free boundary in the obstacle problem. On the first part of the course, we will revisit the classical theory from the 1970’s (although not always following the original proofs). We will start discussing the existence, uniqueness, and optimal regularity of the solutions. Later we will explain some insightful examples of Levy, Kinderleherer, and Niremberg of solutions with singular free boundaries, which are constructed using complex variables. After, we shall prove the existence of blow-ups and their classification leading to the celebrated dichotomy of Caffarelli. Finally, we will discuss how to prove smoothness of the free boundary near points which have blow-ups of regular type.
On the second part of the course, we will introduce some recent developments of the theory regarding the structure of the singular set. We will introduce monotonicity formulae methods and explain why the fine analysis of singularities of the obstacle problem leads to the analysis of singular points for the so called Signorini problem.
Finally, we will prove, in the 2D case, some new results (with A. Figalli) on higher order expansions at singular points. If time allows, we will explain roughly how the content of the course is fundamental in the recent proof in dimensions 3 and 4 of a conjecture of Schaeffer on the generic regularity of the free boundary (in a joint work with A. Figalli and X. Ros-Oton).

Organizing Committee

Xavier Cabré​ ICREA-​Universitat Politècnica de Catalunya-CRM
Gyula Csato Universitat de Barcelona-CRM
Amadeu Delshams​ ​Universitat Politècnica de Catalunya-CRM
​Marcel Guàrdia​ ​​Universitat de Barcelona-CRM
Tere M. Seara​ ​Universitat Politècnica de Catalunya-CRM

Scientific Committee

Scott Armstrong Courant Institute, New York University
Jean Pierre Eckmann ​ ​Université de Genève
​Jean-Michel Roquejoffre ​Paul Sabatier University
​Susanna Terracini ​Università de Torino

List of participants

Name Institution
Mar Giralt Miron
Prosenjit Roy IIT Kanpur
Xavier Tolsa Domènech ICREA and Universitat Autònoma de Barcelona
Ezequiel Maderna Universidad de la República
Giuseppe La Scala Scuola Superiore Meridionale
MARCEL GUÀRDIA MUNÁRRIZ Universitat de Barcelona
Gyula Csato Universitat de Barcelona
Andrew Clarke Universitat de Barcelona
Alejandro Haro Provinciale Universitat de Barcelona
Xavier Ros Oton Universitat de Barcelona
Marvin Weidner Universitat de Barcelona
Clara Torres Latorre Universitat de Barcelona
Marina Gonchenko Universitat de Barcelona
Marc Magaña Centelles Universitat Autònoma de Barcelona
Joan Verdera Universitat Autònoma de Barcelona
Miguel Garrido Universitat Autònoma de Barcelona
Josep M Gallegos Universitat Autònoma de Barcelona
Ignasi Guillén-Mola Universitat Autònoma de Barcelona
Carles Trullàs Fernàndez Universitat Autònoma de Barcelona
Maria Teresa Martinez-Seara Alonso Universitat Politècnica de Catalunya
Xavier Cabré Vilagut Universitat Politècnica de Catalunya
Alexandra Lillo Escuder Universitat Politècnica de Catalunya
Albert Mas Blesa Universitat Politècnica de Catalunya
Joan Solà-Morales Universitat Politècnica de Catalunya
Renzo Bruera Universitat Politècnica de Catalunya
Olli Saari Universitat Politècnica de Catalunya
Amadeu Delshams i Valdés Universitat Politècnica de Catalunya
José Lamas Rodríguez Universitat Politècnica de Catalunya
Pau Martín de la Torre Universitat Politècnica de Catalunya
Vicent Navarro Universitat Politècnica de Catalunya
Jorge Ruiz Cases Universidad Autónoma de Madrid
Iñigo Urtiaga Erneta Rutgers
Thaylon Souza de Oliveira University of Campinas
Luan Vinicio de Mattos Ferreira Silva University of Campinas
Matija Livaic University of Zagreb
Max Goering University of Jyväskylä
Tristan Cheny École Polytechnique
Santiago Barbieri University of Paris-Sud
Alessandro Cosenza Paris Diderot University - Paris 7
Andrey Stavitskiy RWTH Aachen University
Airi Takeuchi University of Augsburg
Alessandra Nardi University of Padua
Francesco Monzani University of Milan
Davide Giovagnoli University of Bologna
Davide Polimeni University of Turin
Irene De Blasi University of Turin
GABRIELE ALFONSO University of Naples Federico II
Roberto Ognibene University of Pisa
Liangjun Weng University of Rome Tor Vergata
Alberto Roncoroni Polytechnic University of Milan
Emanuele Salato Polytechnic University of Turin
Gabriele Fioravanti Polytechnic University of Turin
Lorenzo Baroni Roma Tre University
Filippo Gaia Swiss Federal Institute of Technology in Zurich
Giacomo Colombo Swiss Federal Institute of Technology in Zurich
Matilde Gianocca Swiss Federal Institute of Technology in Zurich
Xiangqian Meng University of Washington - Seattle
Emily Casey University of Washington - Seattle
Ignacio Tejeda University of Washington - Seattle
Dídac Gil Rams Centre de Recerca Matemàtica
Niyaz Tokmagambetov Centre de Recerca Matemàtica
Joaquim Duran i Lamiel Centre de Recerca Matemàtica

poster session information

Participants have the option to contribute with a poster presentation. Posters have to measure 841cm x 1189cm (A0).

To apply, please select the relevant option during the registration process.
  • Deadline: April 18th, 2023.
  • Resolutions will be sent on May 26th, 2023.


The registration fee includes coffee breaks and lunch.

  • You will be asked to create a CRM web user account before registering to the activity through the following link:



In order to increase the number of young researchers participating in this activity, the CRM together with CLAY Institute, offers grants to partially cover the registration fee and lodging on-campus (grant reduced fee: 75€).
To apply, you must complete the registration process. Please go to SIGN IN, choose in the OTHERS section the grant you wish to apply for, you will be asked to attach your CV. Please click on the Reservation option before finishing the process. Applicants will receive the resolution and the information on how to proceed for payment by the deadline indicated below:


Application deadline for grants is April 18, 2023
Notifications will be sent on May 26, 2023
New deadline for payment to confirm acceptance of grant will be June 4, 2023.



IF YOUR INSTITUTION COVERS YOUR REGISTRATION FEE: Please note that, in case your institution is paying for the registration via bank transfer, you will have to indicate your institution details and choose “Transfer” as the payment method at the end of the process.


*If the paying institution is the UPF / UB/ UPC / UAB, after registering, please send an email to with your name and the institution internal reference number that we will need to issue the electronic invoice. Please, send us the Project code covering the registration if needed.

Paying by credit card

IF YOU PAY VIA CREDIT CARD but you need to provide the invoice to your institution to be reimbursed, please note that we will also need you to send an email to providing the internal reference number given by your institution and the code of the Project covering the registration (if necessary).

Lodging information





For inquiries about this event please contact the Scientific Events Coordinator Ms. Núria Hernández at​​